二元二次对角逼近的代数性质

Algebraic properties of bivariate quadratic diagonal approximant

在计算函数的二元二次对角逼近时 ,要计算 3个 (m 2 + 2 m + 1)× (m2 + 2 m + 1)阶的行列式 ,计算量很大。该文给出二元二次对角逼近的对偶性、自变量分式变换下的不变性和对称性 ,利用这些代数性质可以由某些已知函数的二元二次对角逼近 ,而不需要计算 3个 (m2 + 2 m + 1)× (m2 + 2 m + 1)阶的行列式 ,来确定出另外一些相应的函数的二元二次对角逼近。

In related literature, bivariate quadratic diagonal approximant's definition has been given as well as its existence property and explicit expression by using determinant. But when bivariate quadratic diagonal approximants of a function are to be computed,three determinants have to be computed whose order is (m 2+2m+1)×(m 2+2m+1) ,so the computational work is very heavy. This paper presents bivariate quadratic diagonal approximant's duality property, unchanging property of autovariable fractional exchange and symmetry property. By using these algebraic properties,bivariate quadratic diagonal approximant of a function can be obtained and it becomes unnecessary to compute three determinants whose order is (m 2+2m+1)×(m 2+2m+1) .